Finite Group Databasebeta

D47×#1740 #26213707

order12032
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productD47×#1740

Splittings

FittingC47×#1740 ⋊ C2
SylowC47 ⋊ C2×#1740

Subgroups

subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC47×#1740C2
socleC22×C47C22×C22⋊C4
prime radicalC24×D47C23
cosocleC24×C47C24
hypercenter#1740D47
hypocenterC47C2×#1740
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1740

2350 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 166997);